On parameter estimation for Markov sequences and applications in health economics

Overview & Synopsis

In the first part of this dissertation we consider several problems of finite-dimensional parameter estimation for Markov sequences in the asymptotics of large samples. The asymptotic behavior of the Bayesian estimators and the estimators of the method of moments are described. It is shown that under regularity conditions these estimators are consistent and asymptotically normal. We show that the Bayesian estimator is asymptotically efficient. The one-step and two-step maximum likelihood estimator-processes are studied. These estimators allow us to construct the asymptotically efficient estimators based on some preliminary estimators, say, the estimators of the method of moments or Bayes estimator and the one-step maximum likelihood estimator structure. We propose particular non-linear autoregressive processes as examples and we illustrate the properties of these estimators with the help of numerical simulations. In the second part we give theapplications of Markov processes in health economics. We compare homogeneous and non-homogeneous Markov models for cost-effectiveness analysis of routine use of transparent dressings containing a chlorhexidine gluconate gel pad versus standard transparent dressings. The antimicrobial dressing protects central vascular accesses reducing the risk of catheter-related bloodstream infections. The impact of the modeling approach on the decision of adopting antimicrobialdressings for critically-ill patients is discussed.